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<Title>Boost Graph Library: Topological Sort</Title>
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<H1><A NAME="sec:topological-sort">
<img src="figs/python.gif" alt="(Python)"/>
<TT>topological_sort</TT>
</H1>

<PRE>
template &lt;typename VertexListGraph, typename OutputIterator,
          typename P, typename T, typename R&gt;
void topological_sort(VertexListGraph&amp; g, OutputIterator result,
    const bgl_named_params&lt;P, T, R&gt;&amp; params = <i>all defaults</i>)
</PRE>

<P>
The topological sort algorithm creates a linear ordering of the
vertices such that if edge <i>(u,v)</i> appears in the graph, then
<i>v</i> comes before <i>u</i> in the ordering. The graph must be a
directed acyclic graph (DAG). The implementation consists mainly of a
call to <a
href="./depth_first_search.html"><tt>depth_first_search()</tt></a>.
</p>

<h3>Where Defined:</h3>
<a href="../../../boost/graph/topological_sort.hpp"><TT>boost/graph/topological_sort.hpp</TT></a>

<h3>Parameters</h3>

IN: <tt>VertexListGraph&amp; g</tt>
<blockquote>
  A directed acylic graph (DAG). The graph type must
  be a model of <a href="./VertexListGraph.html">Vertex List Graph</a>
  and <a href="./IncidenceGraph.html">Incidence Graph</a>.
  If the graph is not a DAG then a <a href="./exception.html#not_a_dag"><tt>not_a_dag</tt></a>
  exception will be thrown and the
  user should discard the contents of <tt>result</tt> range.<br>
  <b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>

OUT: <tt>OutputIterator result</tt>
<blockquote>
The vertex descriptors of the graph will be output to the
<TT>result</TT> output iterator in <b>reverse</b> topological order.  The
iterator type must model <a
href="http://www.boost.org/sgi/stl/OutputIterator.html">Output
Iterator</a>.<br>

<b>Python</b>: This parameter is not used in Python. Instead, a
Python <tt>list</tt> containing the vertices in topological order is
returned.
</blockquote>

<h3>Named Parameters</h3>

UTIL/OUT: <tt>color_map(ColorMap color)</tt>
<blockquote>
  This is used by the algorithm to keep track of its progress through
  the graph. The type <tt>ColorMap</tt> must be a model of <a
  href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
  Property Map</a> and its key type must be the graph's vertex
  descriptor type and the value type of the color map must model
  <a href="./ColorValue.html">ColorValue</a>.<br>
  <b>Default:</b> an <a
  href="../../property_map/doc/iterator_property_map.html">
  </tt>iterator_property_map</tt></a> created from a
  <tt>std::vector</tt> of <tt>default_color_type</tt> of size
  <tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
  map.<br>

  <b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for
  the graph.
</blockquote>

IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<blockquote>
  This maps each vertex to an integer in the range <tt>[0,
  num_vertices(g))</tt>. This parameter is only necessary when the
  default color property map is used. The type <tt>VertexIndexMap</tt>
  must be a model of <a
  href="../../property_map/doc/ReadablePropertyMap.html">Readable Property
  Map</a>. The value type of the map must be an integer type. The
  vertex descriptor type of the graph needs to be usable as the key
  type of the map.<br>

  <b>Default:</b> <tt>get(vertex_index, g)</tt>
    Note: if you use this default, make sure your graph has
    an internal <tt>vertex_index</tt> property. For example,
    <tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
    not have an internal <tt>vertex_index</tt> property.
   <br>

  <b>Python</b>: Unsupported parameter.
</blockquote>


<H3>Complexity</H3>

The time complexity is <i>O(V + E)</i>.


<H3>Example</H3>

<P>
Calculate a topological ordering of the vertices.

<P>
<PRE>
  typedef adjacency_list&lt; vecS, vecS, directedS, color_property&lt;&gt; &gt; Graph;
  typedef boost::graph_traits&lt;Graph&gt;::vertex_descriptor Vertex;
  Pair edges[6] = { Pair(0,1), Pair(2,4),
                    Pair(2,5),
                    Pair(0,3), Pair(1,4),
                    Pair(4,3) };
  Graph G(6, edges, edges + 6);

  typedef std::vector&lt; Vertex &gt; container;
  container c;
  topological_sort(G, std::back_inserter(c));

  cout &lt;&lt; "A topological ordering: ";
  for ( container::reverse_iterator ii=c.rbegin(); ii!=c.rend(); ++ii)
    cout &lt;&lt; index(*ii) &lt;&lt; " ";
  cout &lt;&lt; endl;
</PRE>
The output is:
<PRE>
  A topological ordering: 2 5 0 1 4 3
</PRE>


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<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
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